A beta regression analysis of COVID-19 mortality in Brazil

Abstract

Brazil was one of the countries most impacted by the COVID-19 pandemic, with a cumulative total of nearly 700,000 deaths by early 2023. The country's federative units were unevenly affected by the pandemic and adopted mitigation measures of different scopes and intensity. There was intense conflict between the federal government and state governments over the relevance and extent of such measures. We build a simple regression model with good predictive power on state COVID-19 mortality rates in Brazil. Our results reveal that the federative units' urbanization rate and per capita income are important for determining their mean mortality rate and that the number of physicians per 100,000 inhabitants is important for modeling the mortality rate precision. Based on the fitted model, we obtain approximations for the levels of administrative efficiency of local governments in dealing with the pandemic.

Highlights

• •We model COVID-19 mortality in Brazil, one of the countries most impacted by the pandemic.
• •We perform a beta regression analysis of state mortality rates to obtain a model with a good predictive ability.
• •We construct impact curves of urbanization rate and per capita income on COVID-19 mean mortality in Brazil.
• •We measure the administrative efficiencies of the state governments in coping with the pandemic.

1. Introduction

COVID-19 is a disease caused by the SARS-CoV-2 (Severe Acute Respiratory Syndrome CoronaVirus-2) virus, which was first discovered in 2019 in Wuhan (China). It started spreading quickly around December 2019, and soon COVID-19 became a global pandemic. It is believed that the virus originated in animals and was latter transmitted to humans. For details on the early stages of the COVID-19 pandemic and its origins, see Liu et al. (2020). The first confirmed case in Brazil took place on February 26, 2020; see Serdan et al. (2020). On January 2, 2023, the total number of COVID-19 cases and deaths exceeded 660 million and 6.6 million worldwide, respectively. Brazil was one of the worst hit countries by the COVID-19 pandemic, with nearly 700,000 deaths from the disease by early 2023. Several variants of the SARS-CoV-2 virus were identified in different parts of the world, including Brazil. The so-called Brazilian variant, also known as P.1, was first seen in the state of Amazonas, Brazil in early 2021.

Freitas et al. (2021) analyzed the impact of the P.1 variant on epidemiological indicators in Brazil by comparing data from the peak of the second COVID-19 wave (January 2021), which was largely due to this variant, with data on the peak of the first wave of the disease (April and May 2020). They showed that in the second wave there was an increase in the proportion of cases of COVID-19 in the younger age groups, the share of women among Severe Acute Respiratory Infection (SARI) cases increased, and there was a noticeable increase in the proportion of deaths. They also note that the case fatality rate among those hospitalized in the population between 20 and 39 years old during the second wave was nearly three times higher than that of the first wave.

A notable aspect of the dynamics of the COVID-19 pandemic in Brazil relates to conflicts that arose and intensified between, on the one hand, the federal government and, on the other hand, state and municipal administrations. In April 2020, the Brazilian Supreme Court ruled that, in addition to the federal government, state and local governments had the power to impose rules for confinement, quarantine, and restriction of transportation and traffic on highways due to the coronavirus epidemic. As a result, the country's 27 federative units (26 states and the Federal District) enforced different mitigation measures to protect their populations. Different federative units implemented different mitigation measures and at different times, which accentuated localized disparities in the severity of the pandemic. There was also intense conflict between the federal and state governments over the adoption of such measures. The federal government argued that they should be minimized, with focus on protecting the elderly and people in high-risk groups. Additionally, the federal government promoted the use of unproven drugs against COVID-19, such as hydroxychloroquine, ivermectin, and nitazoxanide; for details on the lack of evidence for the effectiveness of these drugs, see, e.g., Marcolino et al. (2022), and Reis et al. (2021). The Brazilian president, his political allies and top federal government officials also endeavored to sabotage several well-established interventions, such as social distancing, mask-wearing, and vaccination; see Furlan and Caramelli (2021). The federal government under President Jair Bolsonaro also used the fact that public attention was mostly focused on the pandemic to promote environmental setbacks and controversial changes in norms and legislation. For example, Vale et al. (2021) evaluated relevant legislative actions, environmental fines and deforestation in Brazil, and concluded that the federal government took advantage of the COVID-19 pandemic to deepen a pattern of weakening environmental protection in the country.

The modes of SARS-CoV-2 transmission include airborne, droplet, contact, and fecal-oral transmissions. Indoors droplet and airborne transmission of the virus may be curbed, for instance, through adequate ventilation, routine disinfection of toilets, use of face masks, and social distancing. For details, see Delikhoon et al. (2021). The authors review the literature on SARS-CoV-2 transmission through air. Even the temperature (in Brazil, up to approximately 26 °C) has an impact on the number of COVID-19 cases and, consequently, deaths; see Prata et al. (2020). Giovanetti et al. (2022) presented a phylogenetic and phylogeographic analysis of genomic data from all Brazilian federative units and from a neighboring country (Paraguay) collected up to September 2021. Their results show, for instance, that many independent importations of SARS-CoV-2, especially from Europe, took place up to April 2020 and that during 2020 the country transitioned from a viral importer to a viral exporter. They argue that, as with other respiratory viruses, the spread of the SARS-CoV-2 virus in Brazil was guided by a mix of human mobility and population density.

The amount of COVID-19 deaths depends on many factors, which include the number of hospitals and emergency clinics in the public and private networks, the number of beds in intensive care units in public and private hospitals, the number of doctors relative to the population, urban density, the expansion of the hospital system at the most critical moments of the pandemic through the construction of field hospitals, vaccination campaigns, etc. Riley et al. (2022) used data from the United States to identify which variables have the most impact on the number of COVID-19 deaths. They concluded that population-weighted population density (PWPD), a few ‘stay at home’ metrics, temperature and precipitation, race/ethnicity, and chronic low-respiratory death rate are important for explaining the amount of COVID-19 deaths, especially PWPD and mobility metrics.

There are thus many factors that impact the transmissibility of the SARS-Cov2 virus, the amount of COVID-19 cases, and the resulting deaths. Our focus will not reside on building models that try to explain such dynamics. Instead, we will seek to build a simple regression model with good predictive power such that the few conditioning variables included in the model are able to capture the effects of the aforementioned variables. More specifically, our main goal in this paper is to model COVID-19 mortality rates in the Brazilian federative units. In particular, we seek to build a simple regression model with focus on prediction, i.e., a model that is able to accurately predict state mortality rates using knowledge on just a few explanatory variables. All results are based on a class of regression model tailored for use with doubly-bounded dependent variables. It accommodates distributional asymmetries, accommodates non-constant response variances, comprises two sub-models, requires no data transformation, and will never yield improper (i.e., negative or in excess of one) fitted values/predictions. We use per capita income and urbanization rate as predictor variables for the mean mortality rate. Wealthier states tend to have better health care networks and more capillarity of the health system in regions far from urban centers. Additionally, in states with higher fractions of urban residents, there tends to be greater transmission of the virus and spread of the disease. The fitted model's pseudo-R² exceeds 0.70, being indicative of its good ability to explain fluctuations in COVID-19 mortality rates across federative units.

It is important to highlight what is not captured by the conditioning variables used in our regression modeling: the administrative efficiencies in the different federative units. The differences between predicted and observed mortality rates are approximate measures of the efficiencies of the different state administrations in coping with the pandemic. We compute these quantities. They are crude efficiency measures and are conditional on the fitted model. They provide, nonetheless, an approximation for the different levels of administrative efficiency in tackling the pandemic.

The paper unfolds as follows. In Section 2 we briefly present the class of beta regression models and describe the data used in the empirical analysis. As noted earlier, the model we use is tailored for doubly-bounded random variables. The empirical findings are presented and discussed in Section 3. Finally, some concluding remarks are offered in Section 4.

2. Methods

2.1. Beta regression

We will use the beta regression model introduced by Ferrari & Cribari-Neto (2004) to represent COVID-19 mortality rates in the Brazilian federative units. In particular, we will use what is known as the varying precision beta regression model, which comprises two sub-models. Let Y_t be the tth dependent variable and let μ_t denote its mean, t = 1, …, n. Moreover, assume that the Y_t's are independently beta distributed with parameters μ_t (mean) and φ_t (precision). The beta regression model can be expressed as

$$g_1\left({\mu }_t\right)=\sum _{i=1}^p{\beta }_i{x}_{ti}\text{and}{g}_2\left({\phi }_t\right)=\sum _{j=1}^q{\gamma }_j{z}_{tj},$$

where the β_i's and γ_j's are regression parameters, x_t1 = z_t1 = 1∀t, and the x_ti's and z_tj's are, respectively, mean and precision covariates. The functions $g_1:(0,1)\mapsto \mathbb{R}$ and $g_2:{\mathbb{R}}_{+}\mapsto \mathbb{R}$ are strictly increasing and twice-differentiable; they are known as ‘link functions’. Common choices for g₁ are logit, probit, loglog, cloglog, and cauchit; for g₂, it is common to use log and square root. The variance of Y_t is μ_t (1 − μ_t)/(1 + φ_t). Notice that, for fixed μ_t, it decreases as φ_t increases; that is why φ_t is said to be the tth precision.

The parameters that index the mean and precision sub-models (i.e., the sub-models for μ_t and φ_t) are typically estimated by maximum likelihood. Such estimators cannot be expressed in closed-form. Point estimates can be obtained by numerically maximizing the model's log-likelihood function using a Newton or quasi-Newton non-linear optimization algorithm. For further details on the model, we refer readers to Cribari-Neto & Zeileis (2010) and Douma and Weedon (2019).

There are key differences between beta and standard linear regressions. For instance, the former is naturally heteroskedastic since the variance of Y_t changes with μ_t and φ_t. Also, the beta distribution is quite flexible since its density can assume many different shapes (symmetric, skewed to the right, skewed to the left, flat, J-like, inverted J-like, etc.). A particularly important difference is that in linear regressions (with no interactions between regressors or nonlinear covariates transformations) ∂μ_t/∂x_tj = β_j, a constant, for j = 2, …, p. By contrast, in beta regressions this derivative depends on the values of all mean regressors (including x_tj), on all regression coefficients in the mean sub-model, and on the mean link function. Using this property of beta regressions, we will construct impact curves of two important predictors of the COVID-19 mean mortality rate.

2.2. Data

We use data on the 27 federative units of Brazil. Data on the cumulative number of deaths up to January 1, 2023 (deaths) were retrieved from the Brazilian Ministry of Health using the covid19brazil package for the r statistical computing environment (R Core Team, 2023). Data on the estimated populations in 2019 (pop) were obtained from the Brazilian Institute of Geography and Statistics – IBGE. We use the percentage of population living in urban areas (urb), referring to the 2015 National Sample Survey of Households – PNAD, and per capita Gross Domestic Product × 10⁻⁶ (income) in 2020 (i.e., per capita income in millions of reals); the source of the data is the Brazilian Institute of Geography and Statistics – IBGE. Data on the number of medical doctors per thousand inhabitants in each federative unit in 2022 (doctors) were obtained from the Brazilian Medical Association and Federal Council of Medicine. We also collected data on the federative units’ Municipal Human Development Index relative to 2017 from the United Nations Development Program – PNUD (hdi). The dependent (response) variable is the COVID-19 mortality rate per 100 inhabitants (mort100), i.e., deaths/pop × 100. We work with mortality rates relative to populations and not to confirmed cases since there is a considerable disparity between federative units in the levels of testing and under-reporting of cases; see, e.g., Lima et al. (2022).

The correlation between urb and income (urb and doctors) [income and doctors] is 0.71 (0.75) [0.85]. The minimal and maximal (mean and median) mortality rates are 0.1560 and 0.4431 (0.3133 and 0.3073), the standard deviation being 0.0786. The minimal, mean and maximal values of doctors (income) [urb] are 1.1800, 2.3996 and 5.5300 (0.0150, 0.0313 and 0.0870) [59.6382, 80.7947 and 97.3579]. We note that the states with the smallest and largest mortality figures are Maranhão and Rio de Janeiro, respectively.

It is surprising that the poorest state in Brazil has the lowest COVID-19 mortality rate. Some factors contributed to this good performance. For example, there was decentralization of care in eighteen sub-regions, avoiding massive arrivals of patients from the interior to be treated in hospitals in the capital. Additionally, the vast majority of Emergency Care Units (UPAs) in Maranhão belong to the state administration, in contrast to other states where such management is typically done by municipal administrations. This minimized bottlenecks in patient care since physicians had control over the patients admitted to the UPAs and were able to speed up transfers to medium and high complexity hospitals.

São Paulo and Rio de Janeiro are the two most economically important Brazilian states. They are also the states that receive the largest influxes of passengers on international flights. Using data from 2019, Candido et al. (2020) showed that nearly half of the international passengers enter the country through the São Paulo airport, which is followed by the Rio de Janeiro airport (21%). They have also shown that the share of imported COVID-19 cases by city of destination is highly correlated with the proportion of detected imported cases.

Paravidino et al. (2021) compared the proportions of deaths among COVID-19 hospitalized cases in São Paulo and Rio de Janeiro, with stratification by public and private health services. The authors showed that the lethality among hospitalized COVID-19 patients in Rio de Janeiro is at least double that of São Paulo, for both states and capital cities. They concluded that worse health sector governance in Rio de Janeiro, rather than lack of resources, explains the excess mortality of COVID-19 inpatients in Rio de Janeiro. Additionally, Andrade et al. (2020) researched the profile of COVID-19 hospitalizations the Brazilian Unified Health System (SUS) between late February and June 2020 seeking to identify factors related to in-hospital mortality. They showed that nearly 25% of the hospitalizations resulted in death. They also found that the frequency of in-hospital deaths was particularly high in Amazonas and Rio de Janeiro: 34.1% and 32.1%, respectively; the corresponding figure for São Paulo is considerably lower: 22%.

3. Results and discussion

Our chief goal is to model statewide COVID-19 mortality rates in Brazil. The country was severely hit by the pandemic of COVID-19 and has particular characteristics that make this analysis interesting, such as, for example, the acute conflict between the federal administration and local administrations regarding the adoption of mitigation measures.

We model COVID-19 mortality rates (mort100) per 100 inhabitants in the Brazilian federative units. We seek to find a concise regression model that is able to explain most of the variation in the mortality rates among federative units. As previously indicated, we use the class of varying precision beta regression models. Such models are tailored for random variables that assume values in (0, 1). All computations are carried out using the r statistical computing environment (R Core Team, 2023). Maximum likelihood parameter estimation is performed using the betareg package; see Cribari-Neto & Zeileis (2010).

We estimated many models using as mean and precision covariates income, urb, hdi, and doctors. We also considered interactions between them and nonlinear transformations of such regressors. Model selection was guided by (i) Nagelkerke's pseudo-R² (Nagelkerke, 1991), (ii) statistical tests on the covariates coefficients, (iii) the Akaike and Bayesian information criteria (AIC and BIC, respectively), and (iv) residual half-normal plots with simulated envelopes. Half-normal plots were constructed using 100 simulations and the ‘standardized weighted residual 2’ proposed by Espinheira et al. (2007), the envelopes corresponding to the 0.025 and 0.975 residual quantiles. We use Nagelkerke's pseudo-R² because it is sensitive to the specification of the precision sub-model. For models with similar values of such a measure, we examined the corresponding values of the pseudo-R² proposed by Ferrari & Cribari-Neto (2004), which only considers the mean sub-model, and the correlation between observed and predicted mortality rates.

After exhaustive model selection, we arrived at the following model:

$$g_1\left({\mu }_t\right)={\beta }_1+{\beta }_2{x}_{t2}^{0.75}+{\beta }_3{x}_{t3}^2\text{and}{g}_2\left({\phi }_t\right)={\gamma }_1+{\gamma }_2{z}_{t2}^2,$$

where x₂ is urb, x₃ is income, and z₂ is doctors. Overall, the model selection strategies we used favored all but the cauchit mean link function; they also favored the log precision link. We will proceed with the logit and log links.

The maximum likelihood estimates of β₁, β₂, β₃, γ₁, and γ₂ (standard errors in parentheses) are, respectively, −4.1202 (0.4824), 0.1246 (0.0169), −15.2822 (7.2101), 2.7576 (0.4115), and 0.3024 (0.0475). All regression coefficients are statistically non-null at the 5% significance level when z tests are used. Nagelkerke's pseudo-R² for the fitted model is 0.709. Interestingly, ${\widehat{\gamma }}_2>0$, that is, precision increases with the availability of physicians relative to the population. Fig. 1 contains the residual half-normal plot with simulated envelopes. All residuals fall within the envelopes, and hence there is no evidence of model misspecification or outlying data points. The correct specification of the model is not rejected by the RESET test at the usual significance levels; for details on this test, see Pereira & Cribari-Neto (2014). It is noteworthy that urbanization rate is particularly important for explaining mortality rates: when $x_{t2}^{0.75}$ $(x_{t3}^2)$ is dropped from the model, the pseudo-R² value drops to 0.347 (0.676).

Fig. 1.

Residual half-normal plot with simulated envelopes.

Overall, there is good agreement between observed and predicted mortality rates except for three data points. The fitted model overpredicts the mortality rate of Amapá; the observed and predicted mortality rates are 0.2560 and 0.3566, respectively. By contrast, there is underprediction for Mato Grosso (observed: 0.4309, predicted: 0.3155) and Rondônia (observed: 0.4163, predicted: 0.2867). Except for these three cases, there is good agreement between observed and predicted mortality rates. Prediction is quite accurate for a number of federative units. For instance, observed and predicted: (i) Amazonas, 0.3479 and 0.3374; (ii) Federal District, 0.3926 and 0.3926; (iii) Goiás, 0.3956 and 0.3902; (iv) Mato Grosso do Sul: 0.3923 and 0.3696; and (v) Piauí: 0.2452 and 0.2307.

Next, we will compute the impacts of urbanization rate and per capita income on mean mortality. As we noted earlier, unlike in classical linear regressions, the derivatives of the mean of the dependent variable with respect to the regressors (of the mean sub-model) are not constant; they depend on the values of all regressors and all parameters in the mean sub-model as well as on the mean link function. The impact of each variable is computed by setting the value of the other variable at its first quartile (Q1), median and third quartile (Q3). The impacts of urbanization and per capita income on the mean mortality rate are, respectively,

$$\frac{\partial {\mu }_t}{\partial x_{t2}}=\frac{e^{{\eta }_t}}{{(e^{{\eta }_t}+1)}^2}\times 0.75{\beta }_2{x}_{t2}^{-0.25}\text{and}\frac{\partial {\mu }_t}{\partial x_{t3}}=\frac{e^{{\eta }_t}}{{(e^{{\eta }_t}+1)}^2}\times 2{\beta }_3{x}_{t3},$$

where ${\eta }_t={\beta }_1+{\beta }_2{x}_{t2}^{0.75}+{\beta }_3{x}_{t3}^2$. We estimate them by replacing the unknown parameters with the corresponding maximum likelihood estimates.

The estimated impacts are presented in Fig. 2. The left and right panels are for urbanization rate and per capita income, respectively. The derivative of mean mortality with respect to urbanization rate is positive everywhere, which means that, all else equal, the former increases when there are increases in the latter. Such a derivative increases uniformly and rapidly with urbanization rate which means that the effect of increased urban populations on COVID-19 mortality becomes progressively stronger. The increase is approximately linear up to approximately 80%, and slows down after that point. For reference, the third quartile of urb is 85.83%. That is, the strengthening of the impact of urbanization rate on mean mortality slows down in upper quartile. Interestingly, the level of per capita income has little or virtually no effect on the impact of urbanization rate on the mean mortality rate. As already stated, the higher prevalence of urban populations favors the spread of the SARS-CoV-2 virus, since there tends to be more daily interactions between people and groups of people in such environments. This is reflected in our results, which reveal how increases in the urbanization rate affect COVID-19 mortality.

Fig. 2.

Estimated impacts of urbanization rate (left panel) and per capita income (right panel) on the mean mortality rate.

If increases in the urbanization rate contribute to higher COVID-19 mortality, increases in per capita income have the opposite effect. As we see in the right panel of Fig. 2, the derivative of mean mortality with respect to per capita income is negative everywhere, thus implying that increases in per capita income translate, all else equal, into decreases in the COVID-19 mean mortality rate. Such a decrease is nearly linear. Interestingly, the level of urbanization has little influence on the intensity of such an effect in low-income federative units and noticeable influence in wealthier localities. Richer states tend to have better and more widespread public and private health care networks, and also greater capillarity in their geographical spread. Thus, increases in per capita income lead to reductions in the average mortality rate. Our results reveal that this effect is more intense, it should be noted, for federative units with higher urbanization rates.

As noted earlier, the conditioning variables used in modeling the mean mortality rate capture and synthesize several disaggregated factors that are directly related to COVID-19 mortality. Among the factors that are not captured by such variables one stands out, namely: the efficiency of the state administration in coping with the pandemic. We can thus use the differences between the predicted and observed mortality rates as a proxy for such administrative efficiencies. Positive values are indicative of efficient management of the pandemic, while negative values signal inefficiency. We call such a measure ‘primary efficiency’ because it is a raw, crude estimate of administrative governance. It should be viewed as an approximation to the true efficiencies. Future research should be undertaken to construct more refined and disaggregated measures of efficiency.

The following federative units have primary efficiency higher than 0.04: Alagoas (0.0560), Amapá (0.1006), Bahia (0.0630), Paraíba (0.0498), Pernambuco (0.0739), and Rio Grande do Norte (0.0446). Four states display primary efficiencies below −0.04: Ceará (−0.0441), Mato Grosso (−0.1154), Paraná (−0.0429), and Rondônia (−0.1296); Mato Grosso and Rondônia were particularly inefficient in coping with the pandemic.

It is interesting to note that the governors of the states with the best levels of primary efficiency opposed the federal government of President Jair Bolsonaro while three out of the four states with the worst levels of primary efficiency were led by governors who supported the federal government. As noted earlier, President Jair Bolsonaro actively fought the adoption of mitigation measures during the pandemic and contributed to increased public distrust of the efficacy and safety of COVID-19 vaccines. It is also noteworthy that the primary administrative efficiencies computed from the estimated model negatively correlate with the percentages of valid votes obtained by Jair Bolsonaro in the second (first) rounds of the 2018 and 2022 Brazilian presidential elections: −0.4339 and −0.3942 (−0.4562 and −0.4181), respectively.

The federal government fought the adoption of measures imposed by states and municipalities, such as the mandatory wearing of face masks and social distancing rules. President Jair Bolsonaro also raised doubt on the safety and efficacy of COVID-19 vaccines and sought to promote the use of unproved drugs (e.g., hydroxychloroquine and ivermectin). The president's supporters adopted a similar stance, often with exacerbated intensity. The ideological polarization around scientific and sanitary issues was so intense that unfavorable results from a chloroquine clinical trial led to death threats and animosity towards researchers in the country; see Ektorp (2020). The directors of Anvisa, Brazil's health regulator, also received death threats while the agency deliberated on the approval of COVID-19 vaccines for children. As a consequence of such political and ideological polarization, governors from the same political camp as the president were reluctant, to varying degrees of intensity, to adopt mitigation measures for fear of losing popular support. This is in line with our results, since the estimated primary efficiencies negatively correlate with the percentages of votes obtained by President Jair Bolsonaro in the two rounds of the two presidential elections he disputed (2018 and 2022). He was not reelected in 2022, having lost the election to Luís Inácio Lula da Silva (from the Workers' Party).

It was previously noted that Paravidino et al. (2021) compared the proportions of deaths among hospitalized cases of COVID-19 in São Paulo and Rio de Janeiro, the two most economically important Brazilian states. The authors showed that the lethality among hospitalized COVID-19 patients in Rio de Janeiro was at least double that of São Paulo, for both states and capital cities, and concluded that such a difference was due to worse health sector governance in Rio de Janeiro. This conclusion is supported by our results, since our estimates for the administrative efficiencies of São Paulo and Rio de Janeiro are 0.0335 and −0.0148, respectively.

Political polarization in Brazil has been on the rise since 2013. Episodes of intolerance and political violence have become more frequent, particularly since the 2018 presidential election. Broadly speaking, polarization opposes those who support the Workers' Party (and other smaller center-left and left-wing parties) and those who oppose that party's political agenda. The election of president Jair Bolsonaro in 1998 was largely due to a prevailing sentiment against the Workers' Party and the rejection of other conventional parties. According to Fuks et al. (2020), radical antipartisanship has been a major factor driving political conflicts in Brazil and ultimately led to Bolsonaro's electoral victory in 1998. Our results revealed that such a political polarization translated into how efficiently the sate governors coped with the pandemic. The states with the highest primary efficiency figures according to our results are Alagoas, Amapá, Bahia, Paraíba, Pernambuco, and Rio Grande do Norte. The governor of Alagoas was, in the period under review, affiliated with a centrist political party (MDB), but he opposed the federal government. The governors of the other aforementioned states were affiliated with center-left parties (PDT, Workers' Party, and PSB). The states with the lowest primary efficiencies are Ceará, Mato Grosso, Paraná and Rondônia. The latter three states were governed by politicians linked to center-right or right-wing political parties (Democrats, PSD and PSL, the latter being the political party of President Bolsonaro). The governors of these three states supported the federal government in the period under review.

In 2020 COVID-19 spread quickly throughout Brazil despite the fact that the country has a large public health care system that is jointly run by the local, state, and federal governments. Rocha et al. (2021) have shown that the initial course of COVID-19 deaths in Brazil was mainly determined by existing socioeconomic inequalities, rather than age and health status, with a disproportionate burden on locations with greater socioeconomic vulnerability. Their results were obtained using data from the initial phase of the pandemic and linear regressions. We considered a much wider time window and used beta regressions. Our results showed that the intense regional disparities in the country can, as far as COVID-19 mortality predictions are concerned, be summarized in a few conditioning variables: urbanization rate and per capita income to explain the mean mortality rate, and physicians availability relative to the population to explain the mortality rate precision.

Lin et al. (2022) modeled the number of COVID-19 deaths during the first and second waves of the pandemic in the 20 Brazilian cities with the most deaths. Their predictions matched the number of reported deaths reasonably well. The authors concluded that the effects of vaccination campaigns varied across cites, that reinfection was not crucial for the second wave, and that the relatively high infection fatality rate could be due to breakdowns of medical system that took place in several cities. Their results relate to ours in the sense that breakdowns of the local medical systems are linked to the efficiencies of state and municipal administrations. Recall that our results imply that there was appreciable variability in the levels of administrative efficiency in the different Brazilian federative units.

Liu et al. (2022) investigated regional heterogeneity of COVID-19 in-hospital mortality in Brazil and the effects of vaccination and social inequality. The authors fitted multivariate mixed-effects Cox models using data from late February 2020 to mid March 2022. They concluded that age was the most relevant risk factor for death. Also, illiterate patients were at a higher risk of death than those with a college degree. Overall, their results show that there is considerable regional heterogeneity of COVID-19 mortality in Brazilian hospitals. Our results are in agreement with their findings since there is notable variability region-wise in the variables we used to predict COVID-19 mortality rates. We also showed that there is regional variability in the states’ administrative efficiencies in tackling the pandemic.

The regional heterogeneity in the COVID-19 dynamics pointed out by Liu et al. (2022) reaches into and is related to the political landscape in the country. An interesting aspect of Brazilian geopolitics involves regionalism. The Northeast region is one of Brazil's five regions and comprises nine states (Alagoas, Bahia, Ceará, Maranhão, Paraíba, Pernambuco, Piauí, Rio Grande do Norte and Sergipe). Jair Bolsonaro was defeated in the second rounds of the 2018 and 2022 presidential elections in every state in the region. In fact, it was only in the Northeast region that Jair Bolsonaro received less than half of the valid votes in the second rounds of both presidential elections; he won in all other regions in both instances.

Siqueira and Brandão (2022) note that since 2019 the governors of the Northeastern states have sought to structure a broad coalition grounded in common interests. It characterizes a new regionalism with a center-left political orientation. The authors examine the role of the COVID-19 pandemic as a catalyst and accelerator of such dynamics. They note that a scientific committee of the region (The Scientific Committee of the Northeast Consortium for Combating Coronavirus – C4NE) was established in 2020 to assist governors in monitoring the pandemic and developing health policies. Initially, this committee was led by neuroscientist Miguel Nicolelis and physicist Sergio Rezende. According to the authors, “in relation to other Brazilian regions, the support of the C4NE has resulted in adopting stricter measures against the spread of the virus and more effective communication.”

In order to investigate whether the dynamics of the COVID-19 pandemic were different in the Northeast region relative to other regions, we introduced into the previously fitted beta regression model a dummy variable that equals one for the states in the region and zero for all other states. The extended model (with the dummy variable) was then estimated. We note that the regional effect proved to be statistically significant, the corresponding z test p-value being 0.0176. The pseudo-R² of the regression increased to 0.760 and the dummy coefficient estimate was −0.2738. This negative value indicates that, all else equal, lower mortality rates are expected for the Northeastern states. This fact can be exploited to obtain more accurate forecasts. We computed the mean squared predicted errors (root mean squared predicted errors) from the models with and without the regional dummy variable and obtained, respectively, 0.0022 and 0.0026 (0.0472 and 0.0510). That is, incorporating the regional effect pointed out by Siqueira and Brandão (2022) into the beta regression model led to more accurate predictions: over 15% (nearly 7.5%) improvement in the mean squared prediction error (root mean squared prediction error). It is worth noting that seven of the nine Northeastern states have positive primary efficiency; Ceará and Sergipe are the ones with negative efficiencies. The average efficiency of state administrations in the region is positive: 0.0259. Additionally, as we saw earlier, five of the six states with administrative efficiency above 0.04 are from the Northeastern region.

4. Conclusions

We presented an empirical analysis of state COVID-19 mortality rates in Brazil. Our focus was on developing a model with good predictive power that uses conditioning variables capable of synthesizing the numerous determinants of COVID-19 mortality. We showed that the selected beta regression model has a very good predictive ability. Using the fitted model, we constructed curves that represent the impacts of increased urbanization rate and increased per capita income on COVID-19 mean mortality. Our results revealed that: (i) the positive impact of the urbanization rate on the COVID-19 mortality rate gradually becomes more intense as the urbanization rate increases, (ii) the negative impact of per capita income on the COVID-19 mortality rate is gradually strengthened as per capita income increases, and (iii) per capita income has nearly no effect on the urbanization rate impact on COVID-19 mortality and urbanization rate only has a noticeable effect on the income impact in richer federative units; such an impact is stronger for more urbanized states.

The explanatory variables used in the modeling do not reflect local administrative efficiencies. Thus, the comparison between predicted and observed death rates provides raw estimates of the different levels of managerial efficiency of state administrations in dealing with the COVID-19 pandemic. We computed such primary efficiencies, and identified the federative units with the best and worst responses to the pandemic.

Overall, the reported results showed that it is possible to accurately predict state COVID-19 mortality rates in Brazil using a regression model tailored for use with doubly-bounded dependent variables and only three explanatory variables, namely: urbanization rate, per capita income, and the number of physicians relative to the population.

There are several directions for future research. For instance, it would be useful to construct more refined measures of the federative units’ administrative efficiencies in coping with the COVID-19 pandemic. Additionally, it would be useful to investigate whether more accurate mortality rate predictions can be obtained when more elaborate models are used, including machine learning models.

Declaration of competing interest

The author declares that he has no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Handling Editor: Dr He Daihai